Horizontal Line Test

Autor:mathtasksproj, Carlos

We say

is a 1 to 1 function if whenever

and

we have

. The mathematical term 'injective' is also used for these functions. We say

is an onto function if the range of

is equal to

. The mathematical term 'surjective' is also used for these functions. On the following graph, adjust the values of

to move the line

and find points of intersection between the line and the function

Graph of f(x)

1A)

Is this function 1-1? Explain your answer.

Zkontrolovat mou odpověď

2A)

Are there any intervals for which f(x) is 1-1?

Zde označte odpověď(i)

A
B
C
D
There are no intervals for which the function is 1-1

Zkontrolovat mou odpověď (3)

3A)

Is this function onto? Explain why.

Zkontrolovat mou odpověď

Now consider the function

below:

Graph of g(x)

1B)

Is this function injective? Explain your answer.

Zkontrolovat mou odpověď

2B)

Are there any intervals for which f(x) is injective?

Zde označte odpověď(i)

A
B
C
D
There are no intervals for which the function is 1-1

Zkontrolovat mou odpověď (3)

3B)

Is this function surjective? Explain why.

Zkontrolovat mou odpověď

What features should a graph have in order to represent a 1-1 function? What about an onto function? Test your conjectures by entering a function in the graph below and applying the appropriate tests.

Horizontal Line Test

Graph of f(x)

1A)

2A)

3A)

Graph of g(x)

1B)

2B)

3B)

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